Question

Find the equations to the tangents to the circle
$x^2+y^2=4$ which are parallel to the line $x+2y+3=0$.

Answer 1

Let the equation of tangent be $x+2y+c=0$

The line is at a distance of $2$ from $(0,0)$

$\therefore 2=\frac{0+0+c}{\pm \sqrt{1+4}}$

$c=\pm 2\sqrt{5}$

The tangent is $x+2y\pm \sqrt{5}=0$